Optical Measurement and Control

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Optical Measurement and Control of Atomic Spin
Ensembles
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Thanks to
UA Kim Fook Lee Brian Mischuck Souma Chaudhury W.
Rakreungdet Greg Smith Lori Harrison Kevin Schulz
UNM Ivan Deutsch Andrew Silberfarb
NSF
ARO
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Basics Atom-Probe Interactions
Typical setup
atom cloud
Off-resonance probe
dispersion only
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Basics Atom-Probe Interactions
- what information about the system can we
access? - how does the probe affect the system
evolution?
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Basics Atom-Probe Interactions
- what information about the system can we
access? - how does the probe affect the system
evolution?
atom-probe interaction
atomic tensor polarizability
field
rank-2 tensor operator acting in Fg manifold
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Basics Atom-Probe Interactions
- what information about the system can we
access? - how does the probe affect the system
evolution?
Irreducible tensor decomposition
Scalar
spin polarization-independent
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Basics Atom-Probe Interactions
- what information about the system can we
access? - how does the probe affect the system
evolution?
Irreducible tensor decomposition
Vector

Rotation of F, S around z-axis by angles µ Sz
resp. Fz
Effect on spin rotation µ probe
ellipticity
Effect on probe rotation µ sample
magnetization
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Basics Atom-Probe Interactions
- what information about the system can we
access? - how does the probe affect the system
evolution?
Irreducible tensor decomposition
Tensor
Effect on spin more general evolution
beyond rotations
Effect on probe change of ellipticity
(birefringence)
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Basics Atom-Probe Interactions
- what information about the system can we
access? - how does the probe affect the system
evolution?
Irreducible tensor decomposition
Alkali atoms in large detuning limit D DHF
nuclear spin decouples
We can measure only the components of
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Probing Spins by Faraday Rotation
Simple theory Faraday signal
atom-probe coupling
probe field
- no fictitious B-field - no action on spins -
Faraday rotation of probe polarization
QND measurement!
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Probing Spins by Faraday Rotation
Simple theory Faraday signal
index of refraction
signal power
angle of rotation
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Probing Spins by Faraday Rotation
Simple theory Shot-noise limited resolution
shot-noise equivalent power
resolution limit
smallest detectable spin
information gain
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Probing Spins by Faraday Rotation
Example Larmor precession of Cs atoms in
spin-coherent state
real-time, 108atoms
SNR 470
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Spin Squeezing by Measurement
Compare resolution to Spin-Projection Noise
Collective spin
Mean-Square fluctuations
Spin-coherent state
Spin squeezing if
backaction figure-of -merit
Geremia et al, Science 304, 270 (2004), and next
talk
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Spin Squeezing by Measurement
- optical pumping due to photon scattering
- evolution of spin due to rank-2
tensor part of atom-probe coupling
td few x ts
varies widely
td
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Spin Dependent Light Shift in Alkalis
Calculate total (vectortensor) light shift _at_
finite D
- keep terms to leading order in
DHF/D 17
Nonlinear Spin Dynamics
theory
Modified Larmor Hamiltonian field Bx, probe
pol. along x
Modified Larmor precession
- non-linear term evolution ? rotation
- Integrate Schrödinger eq. collapse
revival
- Master eq. treatment
Silberfarb Deutsch
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Nonlinear Spin Dynamics
Experiment collapse revival
times versus ts gs-1
Modified Larmor Hamiltonian field Bx, probe
pol. along x
Modified Larmor precession
- non-linear term evolution ? rotation
- Integrate Schrödinger eq. collapse
revival
- Master eq. treatment
Silberfarb Deutsch
- NL collapse MUCH faster - than decoherence!
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Controlling the Nonlinearity
Problem
- nonlinear collapse limits useful
measurement time
- measurement time limits backaction
- we need some compensating nonlinear
term
2nd NL light shift?
- in principle yes
- but there is a simpler way!
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Controlling the Nonlinearity
Experiment play around with
geometry
How does it work?
probe geometry
nonlinear light shift
RWA
nonlinearity disappears for
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Controlling the Nonlinearity
collapse/dephasing time vs ts at magic
angle
collapse/dephasing vs angle
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Summary Probing Spins by Faraday Rotation
- Tensor/nonlinear part of probe light shift
important collapse revival in
Larmor precession - Backaction, spin squeezing
limited by nonlinearity - Nonlinearity can be
cancelled useful measurement time
5-10 ts
Smith, Chaudhury Jessen J. Opt. B 5, 323 (2003)
Smith et al. quant-ph/0403096
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Outlook Probing Spins by Faraday Rotation
Eliminate tensor/nonlinear light shift -
recover QND measurement - long measurement
times backaction in moderate OD
samples Enhance use tensor/nonlinear light
shift - increase nonlinearity by tuning to D1
resonance - explore nonlinear spin dynamics
(quantum chaos) - extract more general
information real-time density
matrix reconstruction
Silberfarb Deutsch - implement more general
measurements probe clock
doublet pseudospin
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Probing the Clock Doublet
Atomic clock doublet probe squeeze
pseudospin? atomic clocks, interferometers?
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Probing the Clock Doublet
Problem no Faraday signal from m 0 states
Vector
Answer
Tensor
birefringence
clock doublet
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Probing the Clock Doublet
Level scheme for Cs D1 transition
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Probing the Clock Doublet
Level scheme for Cs D1 transition
- birefringence
upper clock state
- transparant
lower clock state
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Probing the Clock Doublet
Basic measurement setup
PBS
9.2 GHz
Net birefringent signal
Sensitivity comparable to Faraday measurement
- comparable performance -
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Probing the Clock Doublet
Proof of principle measurement of Rabi Flopping
Theory master eq. calc.
Exp single-shot data
time (ms)
- it works! -
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Probing the Clock Doublet
Refinements designing a useful QND measurement
Problem differential light shift
of clock states
inhomogeneous broadening of clock transition
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Probing the Clock Doublet
Refinements designing a useful QND measurement
Solution magic probe freq.
where
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Probing the Clock Doublet
Refinements designing a useful QND measurement
signal from
light shift
signal from
4-4
4-3
3-4
3-3
- QND points -
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Probing the Clock Doublet
Refinements designing a useful QND measurement
Rabi flopping vs. probe frequency
Rabi freq.
decay time vs. D (gs constant)
Master Eq. incl. inhomogeneity
Exp.
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Probing the Clock Doublet
Refinements designing a useful QND measurement
Problem signal measures sz 1, not sz
Angular momentum
z
y
x
squeezing independent of
)
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Probing the Clock Doublet
Refinements designing a useful QND measurement
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Probing the Clock Doublet
Refinements designing a useful QND measurement
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Probing the Clock Doublet
Refinements designing a useful QND measurement
appears feasible to design QND measurement of
clock pseudospin in close analogy to Faraday
measurement of ang. momentum - very similar
measurement performance -
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Application to Metrology
Ramsey Spectroscopy/Atomic Clocks (long shot)
Ramsey interrogation
p/2 pulse
p/2 pulse
measure Sz
Sz

- details to be - filled in
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Application to Metrology
Map clock doublet onto atom interferometer
paths (Kasevich approach)
squeezed state preparation
measure sz
Raman p pulse beamsplitter
Raman p pulse beamsplitter

Raman p pulses
- details to be - filled in